The Gauss-Seidel method is known to be convergent when \(A\) 
is symmetric positive-definite, e.g. [1]}, or strictly or irreducibly diagonally dominant, e.g. [2]}. The case when \(A\)  is only positive semidefinite
(with positive diagonal) seems to be less well-understood, and our approach sheds more light on this case. In particular,
numerical results of the type shown in Figure REF  apply here.
